When actor Peter Jason, who plays Dr. Leahy, introduces himself to Dr. Birack ('Victor Wong') for the first time, he wasn't expecting Wong to walk away in the middle of the scene. Jason's subsequent confused appearance and awkwardness is natural and unscripted.
In the scene where Brian and Catherine are in bed in the morning, Brian says to her, "Who was he, the one that gave you such a high opinion of men?" This is a fairly well known quote (among others) from To Have and Have Not (1944), only the sexes are reversed here. The original has Lauren Bacall saying, "Who was the girl, Steve?" To which Humphrey Bogart replies, "Who was what girl?" And she responds, "The one who left you with such a high opinion of women."
Screenwriter John Carpenter is credited as "Martin Quatermass". The pseudonym is a homage to Professor Bernard Quatermass, the lead character of The Quatermass Experiment (1953) and several subsequent TV series and film versions. In the original press notes he was described as 'the brother of Professor Bernard Quatermass, head of the British rocket programme.' In a further nod to Carpenter's influences, the character Wyndham is named after science-fiction author John Wyndham and Anne Howard's character is named after the star of The Wasp Woman (1959), Susan Cabot.
The audio of the "broadcasts" that Brian receives in his dreams was sampled by Marilyn Manson in the song "Down In The Park" originally performed by Gary Numan. It is also sampled on DJ Shadow's album 'Endtroducing...'
Although the film wasn't John Carpenter's first screenplay that he wrote since Escape from New York (1981), it was the first film since Escape that he directed but credited himself as "Martin Quatermass". A similar thing he did on They Live (1988) but under the name "Frank Armitage".